Answer:
Option 1 correct(55 tickets)
Explanation:
Given that movie theater has 400 seats and ticket at theater cost $8 for students, $10 for adults and $7 for senior citizen. The number of adult ticket sold was 10 less than number of students and senior citizen tickets.
Ticket sales is $3535. we have to find no. of senior tickets sold.
Let x be number of tickets sold for students, y be the number of tickets sold for adults and for senior citizens no. of tickets z.
since movie theater has 400 seats ⇒ x+y+z=400 → (1)
Also, ticket at theater cost $8 for students, $10 for adults and $7 for senior citizen and total sales is $3535 ∴ equation becomes
8x+10y+7z=$3535 → (2)
The number of adult ticket sold was 10 less than number of students and senior citizen tickets which implies y=x+z-10 → (3)
Solving (1), (2), and (3) we get
Substitute value of y in (1) and (2) from eq (3), we get
x+z=205 → (a)
18x+17z=3636
Solve above two equations, we get
Multiply eq (a) by 18 then subtracting in order to eliminate x
18x+18z-18z-17z=3690-3635
⇒ z=55
The number of tickets sold for the senior citizen was 55 tickets.